We present a measurement of the top quark pair (tt¯) production cross section in pp¯ collisions at s=1.96TeV using events with two charged leptons in the final state. This analysis utilizes an integrated luminosity of 224–243 pb−1 collected with the DØ detector at the Fermilab Tevatron Collider. We observe 13 events in the e+e−, eμ and μ+μ− channels with an expected background of 3.2±0.7 events. For a top quark mass of 175 GeV, we measure a tt¯ production cross section of σtt¯=8.6−2.7+3.2(stat)±1.1(syst)±0.6(lumi)pb, consistent with the standard model prediction.